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<p>This paper presents an adaptive coupling method that integrates ordinary state-based peridynamics with the quadtree-based scaled boundary finite element method, specifically developed for modeling porous materials. The adaptive mesh partition is automatically achieved based on a newly developed displacement-induced criterion, in which the SBFEM nodes will be automatically transformed into PD points when the relative displacement between them exceeds a certain critical threshold. The inherent compatibility of SBFEM with quadtree meshes is fully exploited to refine the mesh locally in the critical fracture areas only. A precomputed strategy is adopted, where the stiffness matrices of 16 standard quadtree elements are calculated in advance and cached to avoid redundant computations. The validation cases have demonstrated that the present adaptive coupling method can achieve highly accurate predictions of crack paths in porous plates, and the relative errors are less than 0.8%. Further investigations on random porous media have demonstrated how the pore distribution, size, and density would influence the fracture pattern from single dominant cracks to distributed cracks. The proposed coupling method removes the mesh-size-matching constraint typical of traditional adaptive PD-FEM. Consequently, the FEM domain requires far fewer elements, and a graded mesh transition is effectively achieved. This advancement facilitates the broader application of PD in large-scale engineering.</p>

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Crack propagation in porous materials with an adaptive ordinary state-based peridynamics and quadtree-based scaled boundary finite element method coupling

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Wei Yu,
  • Jun Liu,
  • Tugen Feng,
  • Lei Gan,
  • Xinjian Sun,
  • Binghan Xue,
  • Haibo Wang,
  • Wenbin Ye

摘要

This paper presents an adaptive coupling method that integrates ordinary state-based peridynamics with the quadtree-based scaled boundary finite element method, specifically developed for modeling porous materials. The adaptive mesh partition is automatically achieved based on a newly developed displacement-induced criterion, in which the SBFEM nodes will be automatically transformed into PD points when the relative displacement between them exceeds a certain critical threshold. The inherent compatibility of SBFEM with quadtree meshes is fully exploited to refine the mesh locally in the critical fracture areas only. A precomputed strategy is adopted, where the stiffness matrices of 16 standard quadtree elements are calculated in advance and cached to avoid redundant computations. The validation cases have demonstrated that the present adaptive coupling method can achieve highly accurate predictions of crack paths in porous plates, and the relative errors are less than 0.8%. Further investigations on random porous media have demonstrated how the pore distribution, size, and density would influence the fracture pattern from single dominant cracks to distributed cracks. The proposed coupling method removes the mesh-size-matching constraint typical of traditional adaptive PD-FEM. Consequently, the FEM domain requires far fewer elements, and a graded mesh transition is effectively achieved. This advancement facilitates the broader application of PD in large-scale engineering.